old_dog_learns_old_tricks
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- Joined
- Aug 2, 2016
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- 5
Pulled this out of an old textbook of mine. I'm betting this was easy for me twenty plus years ago but now I'm drawing a blank.
Let \(\displaystyle p_0, p_1, q_0, q_1 \in \mathbb{R}^{+}\).
Let \(\displaystyle \dfrac{p_0}{q_0} < \dfrac{p_1}{q_1} \). Explain why this implies that \(\displaystyle \dfrac{p_0}{q_0} < \dfrac{p_0 + p_1}{q_0 + q_1} < \dfrac{p_1}{q_1}\).
I'm baffled how to deal with that addition in the denominator. Can someone help kickstart my brain? I don't think I need a whole solution if someone can kindly just point me in the right direction.
Let \(\displaystyle p_0, p_1, q_0, q_1 \in \mathbb{R}^{+}\).
Let \(\displaystyle \dfrac{p_0}{q_0} < \dfrac{p_1}{q_1} \). Explain why this implies that \(\displaystyle \dfrac{p_0}{q_0} < \dfrac{p_0 + p_1}{q_0 + q_1} < \dfrac{p_1}{q_1}\).
I'm baffled how to deal with that addition in the denominator. Can someone help kickstart my brain? I don't think I need a whole solution if someone can kindly just point me in the right direction.
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